On the number of limit cycles which appear by perturbation of two-saddle cycles of planar vector fields

Abstract

We prove that every heteroclinic saddle loop (a two-saddle cycle) occurring in an analytic finite-parameter family of plane analytic vector fields, may generate no more than a finite number of limit cycles within the family.Comment: 21 pages, 10 figures, a new section explaining the so called "Petrov trick" in the context of the paper is added. The paper will appear in "Functional Analysis and Its Applications" (2013